A square matrix is said to be a P-matrix if all its principal minors are positive. A square matrix is said to be a Z-matrix if its off-diagonal entries are non-positive.
A matrix \(\mathbb {E}[M(\xi )]\in \mathbb {R}^{n\times n} \)  is called column adequate if for each \(z\in \mathbb {R}^n\) , \(z_i(\mathbb {E}[M(\xi )]z)_i\le 0\)  for all \(i=1,2,\cdot \cdot \cdot ,n\)  implies \(\mathbb {E}[M(\xi )]z=0\) . The matrix \(\mathbb {E}[M(\xi )]\)  is row adequate if \(\mathbb {E}[M(\xi )]^\top \)  is column adequate and it is adequate if it is both column and row adequate [1]}. It is known that a P-matrix is adequate and a symmetric positive semi-definite matrix is also adequate [1]}. However, an adequate matrix may neither be a P-matrix nor a positive semi-definite matrix [1]}.
